How do you simplify root4(93)*sqrt(92)?

1 Answer
SCooke
Jun 4, 2018

You can use logarithms if your calculator cannot do higher-order roots directly.
29.787

Explanation:

.^4√93⋅√92 = 1/4log(93) + 1/2log(92)

Logarithm tables are readily available online and in libraries.

1/4log(93) + 1/2log(92) = 1/4(1.9685) + 1/2(1.9638)

0.4921 + 0.9819 = 1.4740
To convert this back to the desired number, use the exponential function (inverse of logarithm): exp(1.4740) = 10^(1.4740) = 29.787

Direct calculator calculation:
3.1054 xx 9.5917 = 29.787

Related questions
See all questions in Multiplication and Division of Radicals
Impact of this question
1760 views around the world
You can reuse this answer
Creative Commons License